Monday, September 07, 2009

Matt Swartz on home field advantage

Baseball Prospectus's Matt Swartz has completed a nice five-part series on home-field advantage (HFA) in major league baseball. I've always thought HFA was one of the biggest unresolved issues in sabermetrics. So does Swartz, and he said it better than I could:

"[HFA] should surprise us as analysts more than it does. Nearly every study of psychology with respect to baseball has come up revealing either small effects or no effect. We all know that players are human, but the numbers do not seem to indicate many obvious psychological aspects. Hundreds of researchers have tried to discover clutch hitting, but few have found any evidence of its being a repeatable skill. ... We have attempted all kinds of ways to splice the data to reveal a large psychological effect within baseball to show that baseball players don’t behave like statistical models, and there seems to be little evidence of any strong, detectable effects, even if we know they exist and occasionally can discover smaller ones. ...

"However, home-field advantage is perhaps the most obvious area where we see something resembling a psychological effect, or at least an effect that is not captured by our typical models of baseball players and ballgames. It is clear that something about being the home team trumps talent in a way that is mathematically equivalent to benching an average player on the road team."

Swartz proceeds to look at various aspects of HFA. Many of the findings are unremarkable, but there are a couple that are kind of interesting.

First, let me quickly summarize the other stuff that Matt found in each of his five parts.

Part 1: HFA has been very steady over the decades, at around 40 points (.540 to .460). It shows up in almost every statistical category for hitters and pitchers, except those related to errors.

Part 2: There doesn't seem to be a team-specific HFA, except for the Rockies, whose HFA is an outlier and much higher than most.

Part 3: There appears to be a "familiarity" effect. HFA is highest for interleague games, next highest for games between teams in different divisions, and lowest for intradivisional games (where presumably the teams face each other most often). Also, the farther apart the teams, the higher the HFA.

Part 4: The second-last game of a series seems to have a larger HFA than any other game. This apparently only holds for teams who are geographically close together. Lots of other breakdowns show no significant effect.

Part 5: Individual players do appear to show stable HFAs from year to year, suggesting that they can be more or less suited to their home park.

Most of this is roughly in line with what we knew already. But here's the thing I found most interesting: a lot more of HFA comes in the first three innings than in the rest. Here's Swartz's chart; for each inning, the percentages are the difference in runs scored for the home team vs. the visiting team:

1 16.2%
2 9.3%
3 10.1%
4 6.0%
5 7.8%
6 8.1%
7 8.7%
8 6.5%

The overall difference appears to be about 8%. By Pythagoras, if a team scores 8% more runs than their opponents, they'll win a little over 16% more games, which works out to about a .540 winning percentage, exactly as observed (.540 divided by .460 equals 1.17). But the first inning number is huge! If the home team outscored the visiting team by 16.2% overall, its winning percentage would be .575 (Pythagoras with exponent 2).

What could cause this? It could just be that the first inning is higher-scoring overall, and the difference isn't linear. But the difference is still huge. Could this be a real finding, that HFA diminishes later in the game? If it's a question of familiarity, that might make sense, except that why would the visiting team be less familiar with the park the first inning of Game 3 as opposed to the eighth inning of Game 2?

Still, this is something I haven't seen before, and I wonder if you'd find the same thing if you looked at other sports.


One thing that might be good is to break down HFA into its component parts. The articles show us the HFA appears in almost every statistical category, but they overlap. For instance, the home team strikes out less and walks more. This indicates that the visiting pitchers are throwing fewer strikes and more balls. Is that enough to be the entire effect? That is, if the road pitchers are getting behind in the count, the batters will do better, even if batting skill is completely unaffected by HFA. On 2-0, the batters will be seeing juicier pitches, and that alone could account for their extra doubles, triples, and home runs.

Does it? What you'd want to do to find out, is to compare batting lines based on count (and controlling for pitcher, if you really wanted to be thorough). As it stands now, we still don't really know what HFA comes from, whether it's evenly balanced between batter and pitcher, or what.

The home team scores, on average, about 0.4 runs per game more than the visiting team. Using Swartz's numbers and assuming 40 PA per game per team, the home team gets about 0.4 fewer strikeouts and 0.25 fewer walks. That adds up to about .18 runs. That's half the entire effect. Is it possible that just the different (favorable) counts account for the home team's remaining .22 run advantage? Seems possible to me.

Or, looking at it another way: a study I did a few years ago (.pdf, page 4) came up with the figure that turning a ball into a strike is worth about .14 runs. That's a three pitch per game difference between the two teams. Would a three pitch difference (three extra strikes and three fewer balls) be consistent with 0.4 extra strikeouts and 0.25 fewer walks? I don't know, but you could try looking at it that way.

If you went about it that way, you might wind up with a breakdown of HFA something like:

30% pitchers throwing more strikes
15% batters putting the ball in play more often
10% batters hitting a different LD/GB/FB mix
20% higher BABIP on a given type of ball in play
15% more HRs

I'm making these numbers up, of course. And for some of this stuff, you wouldn't be able to tell if it was the pitcher or the hitter; for instance, fewer strikes might just mean that the batter makes contact better, as opposed to the pitcher improving. And for a higher BABIP (which Swartz found), is it the hitters doing better, or the defense doing worse? We don't know. But still, a breakdown like that would be a start.


Another thing I'd like to see is just raw performance data. Do pitchers throw harder at home than on the road? Do their pitches have more break or movement, all else being equal? That might be hard to study, because all else is never equal, and Pitch F/X recorders might be different at different parks. Although, if the Braves' pitchers show 2 MPH more than their opponents at home, but 1 MPH less on the road ... that does indeed tell you something, although the caliber of the opposition might not even out in your two samples.

My guess is that you'd find that HFA goes right down to the most base level imaginable: the home team would have higher bat speeds and pitch velocities. Their players would run faster at home, and they'd have faster reaction times. I suspect that HFA is something universal, and both psychological and physiological. I'd bet that within a few years, evolutionary psychologists will be studying this stuff and have some theories about how we evolved to be physically more competent in familiar surroundings.

But I'm just guessing.

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At Monday, September 07, 2009 9:42:00 PM, Blogger Brian Burke said...

A couple things: The NBA and NFL both show the same tendency in terms of when HFA manifests. NFL teams score almost 55% of the points scored in the 1st quarter, then about 51-52% for the next 3 quarters. Also, NFL HFA is weaker in divisional games. (Divisional opponents play twice a year.)

Evolutionary psychologists have already theorized about this, but they haven't applied it to sports as far as I know. It has to do with game theory, specifically the dove-hawk game. My explanation will seem off-track, but bear with me.

Take a species that mates like a dove--the males just hangs around the females until the others give up and fly off. Imagine that some hawk-like behavior enters the gene pool. (Hawks fight over mates, often in Pyrrhic battles where both combatants are bloodied.) At first the birds with this behavior would successfully chase off all dove-like mating competitors, successfully propagating the "hawk" behavior within the species.

But at some critical point, there will be too many other hawk-like males willing to fight over the females. They end up bloodied and battered, and begin to die off.

Game theory suggests what would happen is that an equilibrium would occur within the species where there was just enough 'hawks' and 'doves' to keep both behaviors stable within the species.

These battles between competitors and behaviors occur in all species and for all kinds of reasons--mating, resources, etc. The battles often kill both competitors, so nature has developed its own system of preserving peace. It's why your dog pees everywhere it can.

Take lions: Lions respect territory. If ever a conflict between males occurs, where the conflict takes place makes all the difference. The lion on foreign territory will give in fairly quickly unless his advantage is severe. Many, many species spend half their day marking and patrolling territory, including our own.

Evolutionary biologists call this 'bourgeois' behavior, because it is similar to our own human culture of respecting property rights and how we settle disputes.

My own hunch is that this is where the psychological aspect of HFA comes from. Humans might have evolved (either genetically or culturally) to modulate their degree of effort or focus based on the familiarity of their surroundings. A 'battle' in an unfamiliar setting might trigger a response to give in more quickly, and vice-versa. Of course, we can cognitively/rationally overcome most of this response, but perhaps not all of it.

Sorry for the long comment. I just think this stuff is really interesting.

At Monday, September 07, 2009 9:47:00 PM, Blogger Phil Birnbaum said...

Thanks, Brian. That stuff is indeed very cool, and it's the first evolutionary psychology explanation I've seen.

I wonder if there are ways to test the dove/hawk theory? I can't think of any: but if it's true, then familiarity wouldn't have much to do with it, would it? I mean, if it's territory, and I get traded to another team and come play at your park tomorrow, it's still your territory and there's no reason for me to play as well as yesterday when it was my territory. So I guess that would be one test.

Any others?

At Monday, September 07, 2009 9:50:00 PM, Blogger Phil Birnbaum said...

OK, this is undoable, but: suppose you had an experiment where you sold Rogers Centre to the Red Sox players. And you gave them keys, and they spent a few days in the off-season there.

And you sell Fenway park to the Blue Jays players, and they do the same thing.

Both teams are encouraged to have the run of the ballpark they own, and they participate in running the place -- deciding where the concessions go, and so on.

HFA should disappear, right? It might even flip and go the other way, might it not?

At Monday, September 07, 2009 10:16:00 PM, Blogger Brian Burke said...

Well, you could do it, sort of. Hurricane Katrina did it to the NFL's Saints and NBA's Hornets. Of course, the sample sizes are pretty low, and as the theory predicts, after a few games the players will acclimate to their new home environment. There might be more examples out there, though.

Just a note, it's not really the dove-hawk theory. It's that the dove-hawk equilibrium is very costly to the species, so a new system evolved--the bourgeois system. It would really be the bourgeois theory of HFA, but I hate that word. Makes me sound like some sort of Marxist!

At Monday, September 07, 2009 10:32:00 PM, Blogger Phil Birnbaum said...

Right, the bourgeois theory.

I suppose you could also play some games in one of the team's minor-league parks. That team should have HFA even if the park is closer to the "visiting" team's home city.

At Monday, September 07, 2009 10:46:00 PM, Blogger Phil Birnbaum said...

Okay, but wait: how would evolution select for being weaker off one's territory than on it? I understand your equilibrium between hawks and doves, but not what forces would select for being weaker on enemy territory.

If some individuals mutated to be weaker on enemy territory, wouldn't they go extinct at the hands of whatever enemies didn't have that trait?

At Monday, September 07, 2009 11:24:00 PM, Anonymous JB H said...

Enjoyed the post.

Very surprised that you didn't bring up the possible effect of umpires. If the HFA can be reduced to a handful of ball/strike calls, then my intuition would be that HFA is almost entirely due to umpires.

Looking for pitch velocity splits seems like the next step. The hit FX data could have the "hitting in worse counts" bias you talk about.

At Monday, September 07, 2009 11:28:00 PM, Blogger Phil Birnbaum said...

Yeah, umpires could be part of it ... I think there was something about that before ... hang on ... yup, here it is:

Do you think umpires are biased three pitches for the home team?

At Monday, September 07, 2009 11:42:00 PM, Anonymous JB H said...

That certainly seems plausible.

If there is no home/away pitch velocity split then I would be pretty confident that the effect is (almost) all umpire. I wouldn't expect pitcher control (a much harder thing to test for) to be effected if velocity isn't.

That would leave the batter's eye and umpires as the possible remaining causes. It doesn't seem likely to me that players would be unaffected by HFA except for the batter's eye.

At Monday, September 07, 2009 11:43:00 PM, Blogger Phil Birnbaum said...

I think the next step would definitely be to look at velocity ...

At Tuesday, September 08, 2009 12:35:00 AM, Blogger Brian Burke said...

The theory is that the hawk-dove equilibrium is a very costly arrangement for a species. It's stable but very expensive in terms of energy, survival, etc. If there is a less costly way to settle the disputes and battles, then that way would be superior. Natural selection would promote the species that operate according to the bourgeois system.

I'm not sure what the actual physiological mechanism is, but I would suspect it's an anxiety response to unfamiliar territory or a heightened adrenal response to competing in familiar territory.

The real big battles are when both competitors believe they are on there own territory.

At Tuesday, September 08, 2009 12:37:00 AM, Blogger Brian Burke said...

Oops. "...their own territory."

At Tuesday, September 08, 2009 12:40:00 AM, Blogger Phil Birnbaum said...

But there's no such thing as group selection, right? Just selection of individuals. And any single individual that mutated to be weaker on others' territory would be less likely to reproduce.

Respecting each other's territory is good for our survival only if both of us do it.

It's like co-operating in the prisoner's dilemma ... if only one of us has the gene to co-operate, we get wiped out. It's only if both of us have the gene that we flourish.

At Tuesday, September 08, 2009 1:48:00 AM, Blogger Hutch said...

I think one thing that people haven't discussed is that people, and athletes especially, are creatures of habit. Meaning that when at home, they have a set routine for whatever they need in order to feel comfortable. Heck, some players have a specific song played in the stadium when they come up to bat.

This comfort level is going to be at its' peak in the first inning. But as the game progresses, it becomes less about comfort and more about talent.

I would like to see what the HFA is in playoff series. Presumably, the team with HFA is the better team overall. Over the course of a 7 game series, the players should become better acclimated to their away location. Would the best way to look at this be to look at series where the lower seed wins one of the 1st two games, thus essentially giving themselves HFA for the rest of the series?

At Tuesday, September 08, 2009 9:56:00 AM, Blogger Brian Burke said...

True. The genetic process of selection has to occur at the individual organism level. However, it can manifest in group dynamics. Schools of fish and flocks of birds are good examples. The individual fish has to evolve an instinct to swim in a school. Those without the instinct don't survive and don't reproduce to pass along their individualist instincts.

Likewise, take a group of early human tribes. Tribes are basically cooperative genetic groupings. The tribes made up of individuals with cooperative instincts will surpass and replace the tribes without the instinct. The concepts of altruism and charity are theorized to have developed this way.

The bourgeois instincts may have developed at the group level as well. Tribes that were constantly warring with others or among themselves over resources eventually may have killed each other off. The tribes with the bourgeois instinct might prosper.

At Tuesday, September 08, 2009 10:42:00 AM, Anonymous Guy said...

I can see five plausible sources for HFA:
1) psychological/hormonal
2) familiarity
3) fatigue/comfort from travel
4) players selected for attributes leveraged by home park (e.g. fast OF in CO)
5) officiating.
The first 3 involve players actually performing better when at home, the other two don't. Anyone have additions?

My view is that the relative weight of these factors probably varies considerably from sport to sport (perhaps reaching 0 in some cases). However, since HFA exists in every sport, one or more of these factors probably exist in all sports.

A few random thoughts:
My guess is that familiarity is the most important factor in baseball, especially the hitting background for batters (also field configurations for fielders). I know Matt found little park variation, but how far back did he go? Today, most parks have pretty standard features. In the past, especially pre-1960s, parks varied much more. My perception is that the Red Sox had large HFAs in the old high-offense Fenway, for example. But I could be wrong. I wonder if there was more park variation in the past?

I've heard that tests have found higher testosterone in soccer players when playing at home. Anyone know of solid evidence for physiological effects like this? Even if there is, I'd expect this effect to be weaker in baseball, because aggression isn't clearly an advantage and because MLB players likely aren't as attached to their "home" town as European soccer players (maybe by this point Derek Jeter has a primal urge to urinate around the edges of the field in New York, but do Teixeira and Sabathia?).

I would love to see someone use the pitch/fx data to see if umps call a tighter strikezone for visiting pitchers. Since K/BB is the biggest difference between home and visiting teams, it's reasonable to suspect a subtle umpire bias at work. (On the other hand, the fact that the HFA hasn't shrunk over the decades as umpiring has become much more prfessionalized would argue the other way.)

At Tuesday, September 08, 2009 10:49:00 AM, Blogger Phil Birnbaum said...

My gut votes:

1. 75%
2. 5%
3. 5%
4. 10%
5. 5%

I think I remember that testosterone study. What if you gave visiting players just a tiny bit of extra testosterone to see what happens? Just for the good of science, you understand. :)

At Tuesday, September 08, 2009 11:41:00 AM, Anonymous Guy said...

Phil: Why do you give so little weight to the familiarity factor? I think it's likely to be important, and Matt's finding that HFA is lower in intra-division games seems to support that.* If it's 75% psychological, shouldn't the HFA be larger intra-division when playing a frequent rival and direct competitor for division titles?

Also, HFA seems to be largest for BBs and Ks, i.e. strikezone judgment by the hitter and/or control for the pitcher. In contrast, there is little/no HFA for HR per FB -- see Tom Meagher's nice article:
None of that seems consistent with the idea that enhanced aggression is at work.

*However, I don't think the huge HFA in inter-league games tells us much unless you control for the DH issue.

At Tuesday, September 08, 2009 3:06:00 PM, Blogger Brian Burke said...

Guy-It could be that the familiarity is causing the hormonal/psychological response. Causes 1 and 2 might be related.

Or, there are really two separate versions of familiarity: One that possibly triggers a physiological/psychological response, and a "structural familiarity" advantage. By
"structural" I mean knowing the ins and outs of the ballpark features--hitting backgrounds, etc., like you suggested.

At Tuesday, September 08, 2009 3:12:00 PM, Blogger Hi said...

People are influenced by others around them without even realizing it. Crowd noise might not influence players too much, but it likely does influence umpires to a very small degree. The travel effect is real. A big reason there is less HFA in divisional games is because of less travel distance. Might be worth looking into when the NFL has screwed up divisions (Atlanta in the west, Tampa in the central etc.)

Interleague play has the DH difference, too

At Tuesday, September 08, 2009 11:45:00 PM, Anonymous Eddy Elfenbein said...

Great post and many great comments. Here are few thoughts to pass along.

This may seem overly linear but the crowd usually seems most pumped-up at the start of a game, and that typically fades as the game wears on.

Also, baseball is an unusual sport since most teams are "fitted" to their stadiums. The Cardinals, for example, were very successful at old Busch stadium despite having some of the lowest home run totals. Since you build your team to your park, it helps you there and hurts you on the road.

At Wednesday, September 09, 2009 10:20:00 AM, Blogger JavaGeek said...

One question I'd like to ask:
What is the average quality of the "pitcher @ home" vs. "pitcher away".

I am familiar with hockey and it is quite common for backups to play more games on the road than at home.

Of course this is in addition to the other effects.

I also know in the NHL schedules are designed to make the home team more successful.

At Thursday, September 10, 2009 12:18:00 PM, Anonymous dq said...

Half of home field advantage is record in one run games.

Years ago, Bill James looked at this and found that about 1/2 of the difference was due to runs scored,and about 1/2 due to diff in pyth.

Majors Last 3 year home win % .556, .542, .546

Pyth (using ^1.72) .523,.511,.518

On average, the home team wins .548, but pytheg is only .517

The difference he surmised was the strategic advantage of batting last.

The record of Home teams in one run games from 2006-2008 (per Baseball-Reference) is 1258-777, so the home team won 240 games more than it "should have", or 80 per year. Based on pyth, the home team won 75 more games than it "should have".

At Thursday, September 10, 2009 4:35:00 PM, Anonymous Nate said...

phil and brian: your bourgeois theory is what i had in mind when i spoke about studies of higher testosterone in home teams versus away teams in soccer matches in previous HFA posts.

brian, you ask what the physiological process is, and i believe the answer is testosterone. if you google: testosterone home advantage, you'll see a few studies out in the field.

phil, you ask about evolution not working on a group level and the term for what brian responded with is called an Evolutionary Stable Strategy. in a population where individuals have different types of strategies, an ESS is one that will survive the test of time in that specific ratio of strategies without breaking down by an invading strategy. a population of 100% individuals playing bourgeois strategy does that.

in essence, the reason animals fight so viciously to defend their territory is that is has the happy side-effect of reducing the number of attacks that occur, which increases your expected "fitness." Suppose you are a rat and you win 50% of battles at home or away. Now suppose that your effort can be tailored to the situation, and you trade in effort on the road for extra effort at home so you win 80% at home and 20% on the road. You would take that deal in a heartbeat, because you will instantly choose to roam around on the road less often. If you roam less often, you will survive more than another 50/50 player. Thus eventually only 80/20 players will be left with many fewer battles. In the end, it's not survival of the fittest, but survival of the battle-shy.

But what about the invader who wants to play hard home or away (try to be 80/80)? Won't he dominate the 80/20 players? The quick answer is yes, but only one on one. In repeated games where he randomly bounces into different players, he will eventually lose to a gaggle of 80/20 players surrounding him. Why? Because he picks fights too much and incurs more total injuries, even if he wins 80% at home and 50% on the road...

the seminal book on this is "Evolution and the Thoery of Games" by John Maynard Smith.

At Thursday, September 10, 2009 5:11:00 PM, Blogger Phil Birnbaum said...

Nate, thanks. Makes sense.

At Wednesday, September 30, 2009 9:07:00 AM, Anonymous Anonymous said...

I'm not sure if anyone is still reading this thread, but I discovered a recently-published book on HFA titled Not in Our House! : A Decade of Home Court Advantage in American Sports by Tom D. Freijo, Ph.D.

The author was interviewed last week on the Under_Score podcast at (you can find it on iTunes) where he discussed some of the findings of his research. He argued that crowd noise was perhaps the greatest contributor to the HFA effect, though he agreed that familiarity and stadium structure were also factors.

Anyway, it sounds like an interesting book and so I thought others reading here may wish to pick it up. The author's web site is at

At Monday, December 06, 2010 1:24:00 AM, Anonymous Anonymous said...

Can't believe these two factors haven't been mentioned here so far, unless I missed it:

- 9th inning.

- Travel. The HFA effect is greater the further away the visiting team is from home, right? What a surprise.


- Familiarity is more than knowing the physical environs and equipment of the ballpark. It's having the entire team support staff at home. It's sleeping in your own home, spending time with your own partner, family or friends, eating familiar meals, etc.

- Park effects, insofar as a team truly can be built for their park; but also familiarity with wind and field conditions. (This is likely to be greatest in the first inning even in a third game. Knowing something you learned yesterday is not the same as being conditioned to it for weeks and years.)

- Possible effects of fan involvement are not measurable by statistical means, and subject only to disputable subjective judgement. Everyone here may want to dismiss fan effects as magical thinking. Pros are trained to be immune to it, but ballplayers differ in psychological makeup and their moods change, like anyone else. No ballplayer is ever going to admit the away fans made him nervous (or that that being booed at home contributed to slumps or errors). They may not realize it themselves. Is it really absurd to think that the bloodthirsty noise from thousands of screaming fans who are either for you or against you can affect the outcome of a few pitches, swings or umpire calls in a game?


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